A generalization of Jeffrey-Hamel problem to Reiner-Rivlin model for energy and thermodynamic analysis using Keller-Box computational framework

This study addresses the heat transport and irreversible mechanisms associated with energy and frictional losses in the Jeffery-Hamel flow of a non-Newtonian fluid adapting the Reiner-Rivlin model. The Reiner-Rivlin model is frequently used to tackle the impact of yield-stresses among the multiple rheological models suggested for constructing the flow of yield-stresses materials. The non-creeping flow between convergent and divergent plates (Jeffrey-Hamel flow), the viscoelastic characteristics of incompressible Reiner-Rivlin liquid are examined by adapting the Navier-Stokes flow. The flow of a Reiner-Rivlin fluid is caused by pressure differential at the inlet. The second law of thermodynamics ultimately provide entropy manifestation. Using a comprehensive Keller-Box approach, self-similar numerical solutions for the velocity and associated fields are provided. The distribution of velocities for fluid-specific characteristics reveals an impedance formed by interaction between wall and diverging flow orientations. Viscous dissipation has a notable impact on the irreversible process and subsequently enhance the transmission of heat. Irrespective of the conduit structure, the Eckert number raises both the centerline and wall temperatures. The wall temperature gradient show a dominant trend for diverging channel. Higher Brinkman number, particularly in the context of the Reiner-Rivlin fluid, render the effect of viscous dissipation on the development of entropy apparent.